Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control
One considers the control problem of an ensemble of Bloch equations (non-interacting half-spins) in a static magnetic field B0. The state M (t, •) belongs to the Sobolev space H 1 ((ω * , ω *), S 2) where the parameter ω ∈ (ω * , ω *) is the Larmor frequency. Previous works have constructed a Lyapun...
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ftccsdartic:oai:HAL:hal-03325203v1 2023-05-15T18:21:45+02:00 Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control Maciel Neto, Ulisses Alves Pereira Da Silva, Paulo Sergio Rouchon, Pierre Amazônia Azul Tecnologias de Defesa S.A. Polytechnic School of the University of São Paulo (Brazil) Universidade de São Paulo (USP) Centre Automatique et Systèmes (CAS) MINES ParisTech - École nationale supérieure des mines de Paris Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) QUANTum Information Circuits (QUANTIC) École normale supérieure - Paris (ENS Paris) Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) This study was financed in part by the Coordenacao de Aperfei¸coamento de Pessoal de Nıvel Superior -Brazil (CAPES) - Finance Code 001. The second author was partially supported by CNPq, Brazil, Project 305546/2016-3, and by FAPESP, Brazil, Project 18/17463-7. This project has received some funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 884762 ). 2021-08-24 https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203 https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203/document https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203/file/autosam.pdf en eng HAL CCSD hal-03325203 https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203 https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203/document https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203/file/autosam.pdf info:eu-repo/semantics/OpenAccess https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203 2021 Lyapunov feedback stabilization Adiabatic control Quantum systems Ensemble controllability Nonlinear systems Bloch equations Control of PDEs [SPI.AUTO]Engineering Sciences [physics]/Automatic info:eu-repo/semantics/preprint Preprints, Working Papers, . 2021 ftccsdartic 2021-12-05T00:04:17Z One considers the control problem of an ensemble of Bloch equations (non-interacting half-spins) in a static magnetic field B0. The state M (t, •) belongs to the Sobolev space H 1 ((ω * , ω *), S 2) where the parameter ω ∈ (ω * , ω *) is the Larmor frequency. Previous works have constructed a Lyapunov based stabilizing feedback in a convenient H 1-norm that assures local L ∞convergence of the initial state M0(ω) to the south pole, solving locally the approximate steering problem from M0 towards the south pole. However, the corresponding control law contains a comb of periodic π-Rabi pulses (Dirac impulses), corresponding to strongly unbounded control. The present work propose smooth uniformly bounded time-varying controls for this local steering problem, where the Rabi pulses are replaced by adiabatic following smooth pulses. Furthermore, simulations show that this new strategy produces faster convergence, even for initial conditions "relatively far" from the south pole. Report South pole Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) South Pole |
institution |
Open Polar |
collection |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
Lyapunov feedback stabilization Adiabatic control Quantum systems Ensemble controllability Nonlinear systems Bloch equations Control of PDEs [SPI.AUTO]Engineering Sciences [physics]/Automatic |
spellingShingle |
Lyapunov feedback stabilization Adiabatic control Quantum systems Ensemble controllability Nonlinear systems Bloch equations Control of PDEs [SPI.AUTO]Engineering Sciences [physics]/Automatic Maciel Neto, Ulisses Alves Pereira Da Silva, Paulo Sergio Rouchon, Pierre Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
topic_facet |
Lyapunov feedback stabilization Adiabatic control Quantum systems Ensemble controllability Nonlinear systems Bloch equations Control of PDEs [SPI.AUTO]Engineering Sciences [physics]/Automatic |
description |
One considers the control problem of an ensemble of Bloch equations (non-interacting half-spins) in a static magnetic field B0. The state M (t, •) belongs to the Sobolev space H 1 ((ω * , ω *), S 2) where the parameter ω ∈ (ω * , ω *) is the Larmor frequency. Previous works have constructed a Lyapunov based stabilizing feedback in a convenient H 1-norm that assures local L ∞convergence of the initial state M0(ω) to the south pole, solving locally the approximate steering problem from M0 towards the south pole. However, the corresponding control law contains a comb of periodic π-Rabi pulses (Dirac impulses), corresponding to strongly unbounded control. The present work propose smooth uniformly bounded time-varying controls for this local steering problem, where the Rabi pulses are replaced by adiabatic following smooth pulses. Furthermore, simulations show that this new strategy produces faster convergence, even for initial conditions "relatively far" from the south pole. |
author2 |
Amazônia Azul Tecnologias de Defesa S.A. Polytechnic School of the University of São Paulo (Brazil) Universidade de São Paulo (USP) Centre Automatique et Systèmes (CAS) MINES ParisTech - École nationale supérieure des mines de Paris Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) QUANTum Information Circuits (QUANTIC) École normale supérieure - Paris (ENS Paris) Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) This study was financed in part by the Coordenacao de Aperfei¸coamento de Pessoal de Nıvel Superior -Brazil (CAPES) - Finance Code 001. The second author was partially supported by CNPq, Brazil, Project 305546/2016-3, and by FAPESP, Brazil, Project 18/17463-7. This project has received some funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 884762 ). |
format |
Report |
author |
Maciel Neto, Ulisses Alves Pereira Da Silva, Paulo Sergio Rouchon, Pierre |
author_facet |
Maciel Neto, Ulisses Alves Pereira Da Silva, Paulo Sergio Rouchon, Pierre |
author_sort |
Maciel Neto, Ulisses Alves |
title |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_short |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_full |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_fullStr |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_full_unstemmed |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_sort |
motion planing for an ensemble of bloch equations towards the south pole with smooth bounded control |
publisher |
HAL CCSD |
publishDate |
2021 |
url |
https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203 https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203/document https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203/file/autosam.pdf |
geographic |
South Pole |
geographic_facet |
South Pole |
genre |
South pole |
genre_facet |
South pole |
op_source |
https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203 2021 |
op_relation |
hal-03325203 https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203 https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203/document https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203/file/autosam.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1766201041417666560 |